Crossover by Cecil Balmond blends maths, engineering, art and architecture and adds a dash of mythology. The result is an interdisciplinary masterpiece

THE work of structural engineer and architect Cecil Balmond tends to polarise opinion. Some of his sculptures and buildings have been hailed as "awe-inspiring" and "beguiling", while others have been reviled as "pornographic" or "Meccano on crack".

Balmond is the non-celebrity half of audacious collaborations, from The Serpentine Gallery Pavilion, London, in 2002 with Japanese architect Toyo Ito to the ArcelorMittal Orbit tower built for London's 2012 Olympics with Turner prizewinner Anish Kapoor.

Now, in Crossover, he chronicles the journey from initial concept and back-of-the-envelope scribbles to some of the most iconic and contentious bridges, buildings and artworks in the world. But the book is much more. It is a genuine effort to unite the interdisciplinary strands of mathematics, engineering, science and architecture. The language is undoubtedly arty and occasionally philosophical, but stick with it. Crossover is far from airy-fairy and may even change the way you view art-speak.

If anyone has the right interdisciplinary pedigree to pull all this off, it is Balmond. Born in Sri Lanka, he studied maths and chemistry and went on to obtain an MSc in advanced structures at Imperial College London. Balmond joined engineering firm Ove Arup in 1968, launching its Advanced Geometry Unit in 2000, and eventually becoming deputy chairman. He left the firm in 2010 to set up his own practice, Balmond Studio.

Balmond is also an author, scooping the Royal Institute of British Architects's Sir Banister Fletcher Prize for the best book on architecture in 2005 for Informal. A book like Crossover, however, involves a delicate balancing act – with the potential to slip into pretentiousness at every turn.

As you might expect, Crossover is a thing of beauty. Fortunately, it has real substance too – packed as it is with pages of photographs, handwritten memos and diagrams, equations and computer-generated geometrics, as well as columns of text.

There are times when Balmond waxes a little too poetic: "The guessing game goes on between shape and form, substance and metaphor. The imagination is primed between a reality of the void and the fiction of its substance."

But this is the authentic voice of the man. I interviewed him in 2011, as the last pieces of cherry red steel were about to be placed on the top of the Orbit. And his talk of the languages and energies of form that we use to construct our own narratives as we experience art or architecture made perfect sense.

Laid out in sections, according to the building or sculpture, Crossover contains just the right mix of artwork and text. One of my favourites is the new China Central Television (CCTV) tower in Beijing. This buckled-over, 234-metre-high skyscraper, with a scary, 13-storey overhang that angles and turns in mid-air, has, as ever, been both celebrated and derided. The New York Timessaid the CCTV headquarters "may be the greatest work of architecture built in this century", but Chinese critics saw it as "pornographic" and the locals simply dubbed it "da kucha" – "big underpants".

The looping skyscraper was designed in collaboration with Rem Koolhaas and Ole Scheeren of Dutch firm the Office for Metropolitan Architecture, and it is fascinating to follow the journey from an initial scribble that climbs straight up the page and turns at right angles, then returns to the ground, through various simulations and structural models before arriving at the finished building.

There is drama as Balmond describes the major challenges – gravity, of course, plus the added complication of building in an earthquake zone. The team addressed these problems by inserting vertical columns and cores to take most of the tower's gravitational load. In addition, they designed the bracing meshwork "skin" that patterns the sides of the CCTV tower. As well as taking some of the load, this is designed to help the building withstand earthquakes. As Balmond puts it: "Not a Great Wall to keep things out but a massive armature to absorb all."

Eventually, the plans satisfied China's seismic design expert review panel. But in the light of 9/11, there was another worry, he recalls: "What if a plane flew into it? We calculated CCTV would survive a direct hit," he says.

The Pedro e Inês bridge in Coimbra, central Portugal, was a simpler proposition. Echoing the fate of the star-crossed lovers after whom it is named, the bridge does not seem to meet in the middle. Balmond explains how he conceived its unconventional form as he flew back to London following a meeting with engineer António Adão da Fonseca, who was leading the project. Balmond describes looking out of the plane window and his eye following the river's eddies and ripples and imagining "another kind of crossing". "All straightness disappears. Meanders take place, small turns. The bridge has no direction to meet," he writes. "I draw two curves. They miss."

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